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Full Idea
Principles of implication imply there is not a purely probabilistic rule of acceptance for belief. Otherwise one might accept P and Q, without accepting their conjunction, if the conjuncts have a high probability, but the conjunction doesn't.
Gist of Idea
I might accept P and Q as likely, but reject P-and-Q as unlikely
Source
Gilbert Harman ((Nonsolipsistic) Conceptual Role Semantics [1987], 12.2.2)
Book Ref
Harman,Gilbert: 'Reasoning Meaning and Mind' [OUP 1999], p.213
A Reaction
[Idea from Scott Soames] I am told that my friend A has just won a very big lottery prize, and am then told that my friend B has also won a very big lottery prize. The conjunction seems less believable; I begin to suspect a conspiracy.
16967 | 'Are Coriscus and Callias at home?' sounds like a single question, but it isn't [Aristotle] |
17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
12010 | Is the meaning of 'and' given by its truth table, or by its introduction and elimination rules? [Forbes,G] |
23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |